Starting in the top left corner in a 20 by 20 grid, how many routes are there to the bottom right corner?

Solution:
A direct computation:

problem_15 =iterate(scanl1(+))(repeat1)!!20!!20

Thinking about it as a problem in combinatorics:

Each route has exactly 40 steps, with 20 of them horizontal and 20 of
them vertical. We need to count how many different ways there are of
choosing which steps are horizontal and which are vertical. So we have: